Forster, Josef:

The Optimal Regulation of Credit Rating Agencies

Munich Discussion Paper No. 2008-14

Department of Economics

University of Munich

Volkswirtschaftliche Fakultät

Ludwig-Maximilians-Universität München

Online at https://doi.org/10.5282/ubm/epub.5169

The Optimal Regulation of Credit Rating

Agencies

Josef Forster�

July 2008

Abstract

Credit rating agencies (CRAs) very often have been criticized for announ-

cing inaccurate credit ratings and are suspected of being exposed to con�icts of

interest. Despite these objections CRAs remained largely unregulated. Based

on Pagano & Immordino (2007), we study the optimal regulation of CRAs

in a model where rating quality is unobservable and enforcing regulation is

costly. The model shows that minimum rating standards increase the social

value of credit ratings. The model also analyzes implications for regulation

in the presence of con�icts of interest between the CRA and the rated clients

by direct bribes and by the joint provision of rating and consulting services.

Keywords: credit rating agencies, regulation, con�icts of interest

JEL Classi�cation: G20, G24, G28

�Ludwig-Maximilians-Universität München, Department of Economics, e-mail:josef.forster@lrz.uni-muenchen.de. The author would like to thank Gerhard Illing and MonikaSchnitzer for valuable comments.

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1 Introduction

Credit rating agencies (CRAs) play a very meaningful role in today�s �nancial mar-

kets. According to Moody�s (2006) - one of the largest CRAs worldwide - , the

volume of rated debt issues increased globally from US$ 3,500 billion in the year

2002 to over 8,000 billion in 2006.1 In principle, credit ratings should serve as

third-party opinions about the solvency of a debt instrument and should reduce the

information asymmetry between an issuer of a debt instrument and the potential

investors, and therefore improve e¢ciency and transparency in �nancial markets.

The CRAs pronounce that their credit ratings should not be interpreted as default

probabilities and that credit ratings are rather opinions about risk only. The higher

is the credit rating of a debt instrument, the less likely it should be to default and

the longer it should take to default. A closer look at corporate scandals and �nancial

crisis during the last years reveals that CRAs have been involved several times and

have been confronted with heavy criticism for publishing inaccurate credit ratings.

Examples are the Asian crisis, where the CRAs gave Thailand an investment-grade

rating until �ve months after the start of the crisis or the Enron case, where the

CRAs gave Enron investment-grade until days before it went bankrupt. Another

recent example for public discussion about the behavior of CRAs is the debacle of

subprime lending in the USA with its impact on �nancial markets globally.2 Fur-

thermore, CRAs very often are confronted with the suspicion of being exposed to

con�icts of interest as mostly the issuers of the debt instrument pay for the credit rat-

ing, which fees account for about 90 per cent of the CRAs� revenues, and as CRAs

o¤er additional consulting services to their clients. Again, the crisis in subprime

1A closer look at the market structure of CRAs shows that the market is dominated by threebig global �rms (Moody�s Investors Services, Standard & Poor�s and Fitch Ratings). According topublished data from Moody�s (see Moody�s, 2006) the global industry market share of the threebig agencies was estimated to be 95% in 2006. The largest CRA is Standard & Poor�s with amarket share of 40%, followed closely by Moody�s with 39% and Fitch with 16%.

2Due to the rise in housing prices the volume of subprime loans increased rapidly. Those loanswhere securitized into mortgage backed securities and again these were securitized into collater-alized debt obligations (CDOs). Those complex debt contracts received a very high rating fromthe CRAs, comparable to government bonds. In the �rst half of 2007 CDOs lost almost 40% oftheir value. In order to limit turbulences, the ECB injected around 200 billion Euro and the FEDaround 40 billion US Dollars emergency liquidity in August 2007.

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lending can serve as an illustration of that issue. The CRAs not only issued credit

ratings for structured �nance instruments, but also supported investment banks in

designing them (see for example Mason & Rosner, 2007).

Despite these objections, CRAs remained themselves largely unregulated, but the

discussion on further regulation is active in the media as well as in institutions of

�nancial market supervision. In 2005 the SEC (securities and exchange commission)

published a report on the behavior of CRAs and issued a concept release on how the

regulation of CRAs should be changed. Amongst others regulation would be needed

for requirements on the quali�cations of rating-analysts, the avoidance of con�icts

of interest in the presence of additional services of CRAs and the current monitoring

of CRAs.3 In 2004 the IOSCO4 published a code of conduct fundamentals for CRAs

in which was proposed amongst others that the quality and integrity of the rating-

procedure should be warranted and that credit ratings should be free from con�icts

of interest.5 In September 2006, the U.S. legislations passed the "Credit Rating

Agency Reform Act 2006", with the goal to improve the quality of credit ratings

"for the protection of investors and in the public interest by fostering accountability,

transparency, and competition in the credit rating industry" (see CRA Reform Act,

2006). After the subprime loan crisis in 2007, the EU-commission and US politicians

blamed the CRAs of being jointly responsible for the �nancial crisis. The EU-

commission considered to react with legal regulations for the credit rating agencies

and also US authorities announced to investigate the role of CRAs in the subprime

loan crisis that was set o¤ in August 2007. However, very little progress has been

made in implementing those proposals in national laws and regulations.

This paper contributes to the question whether CRAs should be regulated and

especially concentrates on the allegation of inaccurate credit ratings and adverse

e¤ects of con�icts of interest. The paper studies the optimal regulation of CRAs

in a model where rating quality is unobservable and enforcement of regulation is

costly. The applied theoretical model is based on Pagano & Immordino (2007), where

3see Ba�n (2004)4The IOSCO (International organization of securities commissions) is a union of national insti-

tutions of �nancial supervision of over one hundred countries.5see IOSCO (2004) and Ba�n (2004).

3

the regulation of auditing �rms is analyzed. The model considers a representative

investment bank6 that wants to invest in a risky portfolio and needs to raise debt

from external investors to �nance the investment. A CRA has a costly evaluation

technology and issues a credit rating for the debt contract, which is made available

for external investors. The credit rating is based on the risk of the underlying

portfolio and a credit rating is being issued, if a CRA is assigned by the investment

bank. In the setup, the external investors use the credit rating for their investment

decision and the credit rating helps to allocate investment more e¢ciently, compared

to the case without a credit rating. If rating quality is unobservable, the CRA has

an incentive to lower the rating quality, because the costs can then be reduced and

hence the pro�ts increased.

The model motivates a rationale for regulation by showing that due to the un-

observable rating quality the allocation of investment becomes ine¢cient and social

welfare ine¢ciently low. In a next step a regulator with a costly technology may de-

tect compliance with a minimum rating standard with a certain probability. Being

benevolent, the regulator decides on the minimum rating standard and the costly

detection e¤ort employed in regulation in order to maximize social welfare. The

introduction of regulation leads to the trade-o¤ that more e¢cient allocation of

investment leads to a rise in social welfare, but because regulation is costly, to a re-

duction in social welfare. The results show that the optimal rating standard is lower

than the �rst-best rating quality. In order to give consideration to the fact that

CRAs may be exposed to con�icts of interest, the model is extended in a next step

by assuming that the rated issuer may bribe the CRA in exchange for a better credit

rating and that CRAs do not only rate but also have the ability to o¤er consulting

services.7 It will be shown that with the joint provision of ratings and consulting

services the possibility of collusion may arise, which could have negative e¤ects on

social welfare. The model shows that on the one hand the regulator could get rid

6By using an investment bank in our model setup we give consideration to the extensive publicdiscussion about the role of credit rating agencies in the subprime loan crisis in 2007. Our modelof course can be generalized by using the term "�rm" or "�nancial intermediary", that has a riskyinvestment project and needs external funds to �nance the project.

7Associated with the subprime loan crisis in August 2007, CRAs were under suspicion to givetoo favourable credit ratings for structured debt products, because CRAs did not only rate theproducts, but also were involved in designing products with a good credit rating.

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of the collusion problem by forbidding the joint provision of ratings and consulting

services, but on the other hand that this may not always be optimal from a welfare

perspective. That paper contributes to the theoretical literature on CRAs by �lling

the gap on the optimal regulation of CRAs and by giving consideration to broadly

discussed issues regarding the alleged inglorious role of CRAs in �nancial markets

in the recent past.

The remainder of this paper is organized as follows: Section 2 presents a re-

view of the related literature about the role of CRAs in �nancial markets and the

regulation of CRAs. Section 3 introduces the framework of the model, motivates

the rationale for regulation when rating quality is unobservable and analyzes the

optimal regulation. In section 4 the model is extended by introducing con�icts of

interest between the issuer of the debt instrument and the CRAs which may emerge

by the joint provision of ratings and additional consulting services. Finally, section

5 concludes.

2 Related Literature

Richard Cantor (2004) points to the fact that the literature on the role of CRAs has

almost exclusively an empirical focus. In the small category of theoretical literature,

Millon & Thakor (1984) analyze the rationale, why CRAs exist and motivate their

existence with the possibility of information and risk sharing. They conclude that

CRAs might not have an incentive to employ costly e¤ort into the process of inform-

ation production. However, neither con�icts of interest nor regulation of CRAs are

considered. Regulation is not considered either in Kuhner (2001), who analyzes the

role of CRAs in times of enhanced systemic risk, where CRAs act as frontrunners in

a Bayesian herding process. Boom (2001) concentrates on the demand and the price

for a rating of a monopolistic rating agencies. But again, no regulatory issues are

incorporated explicitly in the model. Mostly related with our approach is the contri-

bution of Mukhopadhyay (2004), where moral hazard aspects are considered. That

paper motivates the moral hazard problem with unobservable evaluation standards,

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which CRAs use in the rating process, and show, somewhat questionable from a

policy perspective, that a regulator can enforce an evaluation standard with incent-

ive payments to the rating agency. But again, this contribution neither considers

con�icts of interest between the CRA and the rated �rm nor welfare implications

of regulation. Another interesting theoretical motivation for the role of CRAs in

�nancial markets is Boot et al. (2006). They show that credit ratings can act as a

coordination mechanism in the presence of multiple equilibria and that credit ratings

then have the ability to improve �nancial market stability. Despite those valuable

results, issues regarding possible con�icts of interest, moral hazard and regulation

of CRAs are not addressed in this paper. As will be shown in section 3 in more

detail, credit ratings of CRAs and auditing reports of auditing �rms are products

with related characteristics. Hence, the framework of analyzing the behavior and

regulation of auditing �rms is closely related to the analysis of CRAs. Dye (1993)

analyzes the role of auditing standards and litigation against auditors. They derive

auditors� responses to auditing standards and optimal liability rules. Pagano & Im-

mordino (2007) extend the analysis of auditing �rms by focusing on unobservable

auditing quality, con�icts of interest and optimal regulation.

3 The Model

This section introduces a framework for analyzing the regulation of credit rating

agencies. The model is based on Pagano & Immordino (2007), where the optimal

regulation of auditing is analyzed, and on Dye (1993), who studies the relationship

between auditing standards and auditor�s wealth. The rationale for regulation will be

derived by the assumption that the quality of credit ratings is neither observable nor

contractible. It will be shown that a minimum rating standard, set by the regulator,

can improve the outcome from a welfare perspective. The regulatory issues for

auditing �rms in Pagano & Immordino (2007) are closely related to those of CRAs.

Similar to CRAs, auditing �rms serve as information providers for investors and

are assigned and remunerated by the audited �rm. One di¤erence is that auditing

�rms provide information to shareholders, who provide equity, whereas the CRAs

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provide information to investors, which provide debt �nance. Another di¤erence is

that �rms are legally forced very often to be audited whereas getting rated is mostly

voluntary. At last, the product of auditing �rms and CRAs is di¤erent from a legal

perspective. As mentioned in the introduction, until today a credit rating has to be

regarded as an opinion on the default probability only, whose accuracy cannot be

sued by the clients of the CRA in contrast to auditing �rms.8

At �rst we construct a benchmark model with the assumption that the rating

quality is observable and contractible. After relaxing this assumption, we show

in a next step that the equilibrium rating quality becomes ine¢ciently low. By

introducing a regulator with a costly detection technology, we show that a minimum

rating standard improves e¢ciency in the allocation of investment and that welfare

will be increased. Taking into account that CRAs in the real world have often been

blamed to pro�t from market power, we extend our analysis by distinguishing the

cases of perfect competition and market power in the CRA sector.

3.1 Investment Bank, Investors, and the Credit Rating

Agency

We assume an environment with universal risk neutrality and a continuum of in-

vestment banks (IB). A representative IB has the possibility to invest in a risky

portfolio. To �nance investment of the portfolio, it has to raise debt �nance d from

external investors.9 The goal of the representative IB is to maximize its pro�ts from

its investment possibilities. Without debt �nance, we assume that the IB is not able

to invest and the �nal pro�t of the IB would then be zero.

The risk of the portfolio can be characterized as follows: the �nal return of the

portfolio may turn out to be high or low, so there are two possible states (s) of

the portfolio s = g (good) or s = b (bad). The type of the portfolio is a priori

8In the aftermath of the Enron debacle, CRAs avoided regulatory scrutiny and litigation incontrast to auditing �rms, who were convicted to pay high �nes. Also the regulatory oversight ofauditing �rms was strengthend in contrast to CRAs (see for example Zachariahs, 2007).

9We assume that the IB has no own funds initially and therefore has to �nance its operationentirely via debt. To keep the model tractable, we assume that external investors require an interestrate of zero.

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unknown to the IB. If the portfolio is in the good state, its �nal value e is given

by a high payo¤ g, and if the portfolio is in the bad state, the �nal value e is

given by a low payo¤ b. We assume that each investment bank in the economy

invests only in one portfolio in one period. Therefore, the �nal value of the portfolio

is equal to the gross pro�t of the IB in one period. The portfolio will be in the

good state with unconditional probability p and in the bad state with probability

1 � p. Since we assume a continuum of IBs, the unconditional probability p is

also the fraction of IBs in the economy, which has the possibility to invest in a

good portfolio.10 We assume that p is exogenous and a priori known by the IBs

and the external investors and that neither IBs nor investors have further private

information about the quality of the portfolio. If the portfolio is in the good state,

the payo¤ is assumed to be higher than the required debt repayment to the investors

d, but if the project turns out to be in the bad state, the payo¤ is assumed to be

lower than d: g > d > b. Given that the fraction of good IBs p is publicly

known, the expected unconditional gross pro�t of the representative IB is given by

� = pg + (1� p)b. We assume that the expected gross pro�t of the IB exceeds

the required debt repayment (� > d). Therefore, risk neutral investors are willing

to provide debt �nance, given the information about p. Obviously, all IBs that seek

debt �nance, will be served irrespective if their portfolio is actually good or bad.

The representative credit rating agency (CRA) has a costly technology that

enables the CRA to distinguish, whether an IB has the possibility to invest in a

good or a bad portfolio. A single CRA is assumed to rate only one portfolio per

period. The CRA is able to detect a signal about the state of the IB�s portfolio and

accordingly issues a credit rating r that re�ects whether the bank�s portfolio is good

or bad. If the CRA comes to the conclusion that the portfolio is good, it issues a

good credit rating r = g and reversely a bad credit rating r = b.11 Since the rating

technology is costly, the CRA charges a rating fee � from the rated investment bank.

The issued credit rating, which is made available to external investors, in�uences the

10In the paper we will analogously use the terms "good" IB and "bad" IB.11A good credit rating r=g can be regarded as re�ecing an "investment grade" credit rating and

a bad credit rating r=b as a "speculative grade" credit rating.

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expected pro�ts of the IB and the decision of the investors to provide debt �nance.12

According to Dye (1993)13 we assume that the CRA can choose the precision of the

signal about the state of the rated portfolio. We interpret the precision of the CRA

as the quality of a credit rating q. The quality of a credit rating can be interpreted as

the quali�cation of the sta¤, the information technology or the internal organization

of the CRA. The CRA can choose the quality of the credit rating q 2 [0; 1]. The

rating technology is assumed to be perfectly accurate, if the CRA observes a good

signal, but that it may be inaccurate after observing a bad signal. The conditional

probabilities that the issued credit ratings after observing a good and a bad signal

are correct are given by:

Pr(r = g j s = g; q) = 1 (1)

Pr(r = b j s = b; q) = q

It is obvious that the credit rating is always accurate in the case of a good signal.

In the case of a bad signal, the accuracy of the credit rating increases with the quality

that is employed in the rating process. The technology of the CRA can be described

in such a way that credit ratings are biased upwards, meaning that after observing a

good signal, the credit rating is perfectly accurate, but after observing a bad signal

only with a certain probability. In the case of a bad signal, the CRA will issue an

inaccurately good credit rating with a probability (1 � q), while the probability of

issuing a bad credit rating after observing a good signal is zero.14

Given the technology of the CRA, the conditional probability of a rated portfolio

being in a bad state after getting a bad credit rating can be calculated using Bayes�

rule:

Pr(s = b j r = b) =Pr(s = b \ r = b)

Pr(r = b)= 1;

12Since we assume that an IB invests in only one portfolio for which it seeks external �nance,the rating of the portfolio is identical to a rating of the IB itself. Unlike in reality, the model doesnot discriminate between issuer and issue credit ratings.13The assumptions on the rating technology of the CRA are based on Dye (1993), who analyzes

the relationship between auditing standards, auditor�s wealth and litigation.14With that assumption about the technology of CRA we take into account the real world

criticism that CRA may issue too favourable ratings and that ratings may be inaccurately adjustedin the case of a deterioration of an instrument�s or a �rm�s conditions.

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while the conditional probability of a portfolio with a bad credit rating, being in

a good state is given by:

Pr(s = g j r = b) = 0:

The probability that the rated IB is in a good state, conditional on a good credit

rating, is given by the following expression:

Pr(s = g j r = g) =Pr(s = g \ r = g)

Pr(r = g)=

p

p+ (1� p) (1� q);

while the probability that the rated IB is in a bad state, conditional on a good

credit rating, is given by:

Pr(s = b j r = g) =(1� p) (1� q)

p+ (1� p) (1� q):

Using the conditional probabilities above, the expected �nal pro�t of the rated

IB after deduction of the debt repayment to external investors d, conditional on a

good credit rating, can be formulated as:

E (r = g) = Pr(s = g j r = g)g + Pr(s = b j r = g)b � d

! E(r = g) =pg + (1� p) (1� q)bp+ (1� p) (1� q)

� d � � d: (2)

and the expected �nal pro�t of the rated IB, conditional on a bad credit rating

can be written as:

E (r = b) = Pr(s = g j r = b)g + Pr(s = b j r = b)b � d

! E (r = b) = b � d < 0:

Given the technology of the CRA, the expected pro�t of the rated IB in the case

of a good credit rating is larger than the expected pro�t without a credit rating (see

equation (2)). Conversely, the expected value of the IB with a bad credit rating is

smaller compared with the case without a credit rating (b < ). Since b < d, it

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is rational for the external investors not to provide d and the �nal expected pro�t

in the case of a bad rating is zero (E (r = b) = 0). It is obvious that investment

will only take place in the cases of a good credit rating or without a credit rating,

since the expected pro�t of the IB is positive in these two cases, meaning that the

investors get back their funds. In the case of a bad credit rating investors are not

willing to provide debt �nance.15

The question on hand is: when is the IB willing to obtain a credit rating from a

CRA? The IB can only observe the unconditional probability p and is only willing

to pay a rating fee � for a credit rating, if the expected pro�t with a credit rating

is larger than the expected pro�t without a credit rating. The expected pro�t with

credit rating net of the rating fee is given by:

�R = Pr (r = g)E(r = g) + Pr(r = b)E(r = b)� �:

If no credit rating is assigned, the expected pro�t is given by: �n = � d. The

expected pro�t of a credit rating for the IB (�IB) that can be interpreted as the

"informative value" is therefore given by:

�IB = �R � �n (3)

! �IB = q (1� p) (d�b)� � (3�)

If equation (3) is larger or equal zero��IB � 0

�, a credit rating has informative

value and it is then optimal for the IB to obtain a credit rating.16 If instead equation

(3) would be negative��IB < 0

�, the credit rating has no informative value and

henceforth the IB would decide not to assign a credit rating. In that case, credit

ratings do not play a useful role. From equation (3) can be derived that the value

added of a credit rating is increasing in the quality of the credit rating q, decreasing in

15The pivotal criterion for external investors is the expected pro�t of the IB. The group ofexternal investors is assumed to be homogenous and they are not restricted by regulation to investonly in products with a certain credit rating.16We assume that credit ratings are not mandatory. If equation (3) is zero, the IB is indi¤erent

between getting a rating or not. In case of indi¤erence we assume that the IB chooses to obtain acredit rating.

11

Figure 1: Interactions between CRA, IB, and investors.

the unconditional probability p and the rating fee �. If the fraction of good portfolios

becomes larger, the informative value of a credit rating decreases. Furthermore,

equation (3) is increasing in the term (d�b), which can be interpreted as a measure

of potential misallocated investment that can be prevented by a credit rating of a

CRA about the IB�s portfolio. The larger the possible misallocation, the higher

is the value of the credit rating. To simplify notation in the following, we de�ne

m � d � b. We assume that the parameters p, �, b and d are public observable

and given exogenous. Hence, the value of equation (3) depends on the rating quality,

which is set by the CRA. Obviously, if the rating quality would be observable for the

IB, the IB would be able to observe the exact value of the credit rating via equation

(3), while it is not the case if rating quality would be unobservable. We take a closer

look at that issue in part 3.2. Figure 1 summarizes the interactions between the

three agents - IB, CRA and external investors - in the framework of the model.

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3.2 Demand and Supply of Observable and Unobservable

Rating Quality

We assume that the CRA produces only one credit rating per period and that it

faces costs per rating c(q), which are increasing and convex in the rating quality q.17

Revenues are created by charging a rating fee � from the rated IB. Regarding the

setting of the rating fee we distinguish the case of perfect competition and market

power in the sector of CRAs.

i. More CRAs than clients: If there are more CRAs than clients in the

economy, the situation can be regarded as perfect competition among CRAs. In that

scenario, the CRA would set the rating fee equal to the costs per rating: �(q) = c (q)

and therefore make zero pro�ts. If the quality of the credit rating is observable and

contractible, the IB would demand a rating quality that maximizes the additional

pro�t of getting rated in equation (3) that includes the rating fee �(q). We have

assumed above that the costs per rating are increasing and convex in q. Since the

rating fee � has to cover the costs per rating, the rating fee is increasing and convex

in q, too. Due to the convexity of c, the IB�s pro�t from getting rated��IB

�,

expressed in equation (4), is concave and maximization with respect to the rating

quality leads to an internal maximum:

maxq�IB (q) = q (1� p)m� c (q) (4)

The �rst order condition is given by:

(1� p)m = c0 (q) (5)

If the rating quality would be observable and contractible, the IB would require a

quality, where the marginal cost of increasing the rating quality equals the marginal

revenue of a higher rating quality. Solving the �rst order condition for q leads to

17The cost function has the following properties: c0(q) > 0, c00(q) > 0 with limq!0

c�(q) = 0 and

limq!1

c�(q) =1, and c(0) = 0.

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the �rst-best rating quality q� 2 [0; 1]. The characteristics of the �rst-best rating

quality are summarized in proposition 1.18

Proposition 1 If rating quality is observable and contractible, the �rst-best rating

quality q� becomes smaller, if the unconditional probability of the IB�s portfolio being

in a good state p increases and becomes larger, if the size of the potential misalloca-

tion of investment m without a rating increases. The �rst-best rating quality becomes

larger, if the marginal costs per rating c0 (q) become smaller.

Proof. See appendix A.1.

The value of getting a credit rating becomes larger, if the fraction of good port-

folios in the economy decreases. Therefore it is optimal for the IB to demand a

higher rating quality and to pay a higher fee for the CRA�s rating service. From the

optimality condition (5) it is obvious that a credit rating becomes more valuable,

the higher is the potential loss m, if the IB�s portfolio turns out to be in a bad state,

expressed in a higher amount of debt relative to the portfolio�s payo¤ in the bad

state. Therefore, a higher rating quality will be demanded by the investment bank.

The last point of Proposition 1 refers to the cost e¢ciency of CRAs. If the cost

e¢ciency of CRAs increases - meaning lower marginal costs per rating for a given

quality - IBs would demand a higher rating quality. From a welfare perspective, the

IB�s individual gains from getting a credit rating can be interpreted as the "social

value" of a credit rating, where the �rst-best rating quality q� maximizes the social

value of a credit rating.

ii. More clients than CRAs: If in the economy are more IBs than CRAs

there is market power on the side of CRAs. In that case, the rating fee, required by

the CRA, increases as follows. In order to maximize its pro�ts from "producing"

a credit rating, the CRA will set the rating fee to the highest possible level. It

optimally sets the rating fee such that it is equal to the informative value of a credit

18All proofs are located in the appendix.

14

rating for the rated investment bank in equation (3):

� (q) = q (1� p)m

Since we assume that credit ratings are not mandatory, the IB is willing to obtain

a credit rating, if the informative value of the rating minus the rating fee is larger

or equal zero. In case ii. the expected additional pro�t for the IB of getting rated

will be zero. If the IB would set a higher rating fee, the IB would not be willing

to obtain a credit rating. The decision problem of the CRA is now to choose a

rating quality that maximizes its pro�t - the di¤erence between the fee per rating

and the costs per rating: �CRA (q) = q (1� p)m � c (q). Given the fee setting

behavior above, the maximization problem is exactly the same as in case i. (see

equation (4)) and therefore the supplied �rst-best rating quality that maximizes

the pro�ts of the CRA is the same (q = q�). The only thing that di¤ers, is the

distribution of the pro�ts originating from the credit rating. In case i., only the IB

pro�ts from getting rated, while in case ii., the value of the credit rating is taken

entirely by the CRA. The overall social surplus of a credit rating is the same in both

cases. Therefore, the characteristics of the �rst-best rating quality in equilibrium,

as described in proposition 1, applies for the case of market power of CRAs, too. It

has often been a point of criticism in the real world that CRAs have market power

and that the quality of credit ratings would be higher if there were more competition

in the rating sector. As was shown above, the model concludes that market power

in itself is no reason for regulatory intervention if rating quality is observable and

contractible, since the optimal rating quality is the same in the monopoly and the

perfect competition case.

However, the equilibrium rating quality would change, if the rating quality be-

comes unobservable and not contractible. In that case the CRA has an incentive

to lower rating quality after it was assigned to issue a credit rating, because this

would reduce the rating costs and increase the pro�ts. The model does not consider

a repeated game or a reputation mechanism, instead the model concentrates on pos-

sibilities of regulation in a one period game. Therefore, it is even optimal for the

15

CRA to set the rating quality equal zero after it was hired for a rating service by

the IB, because this would maximize the pro�t per credit rating. According to the

rating technology, the CRA would in the case of a rating quality of zero issue inac-

curate good credit ratings and the social value of credit ratings would vanish. The

misallocation of funds therefore increases in the case of unobservable rating quality

and a rationale for regulation emerges in order to preserve the potential social value

of credit ratings. Real world experience - as presented by anecdotal evidence in

the introduction - has shown that the threat of losing reputation alone obviously is

not enough to discipline the CRAs. Partnoy (1999) argues that CRAs "have not

maintained good reputations, based on the informational content of their credit rat-

ings. Instead, credit rating agencies have thrived, pro�ted, and become exceedingly

powerful because they have begun selling regulatory licenses, i.e. the right to be in

compliance with regulation." The next section analyzes the optimal regulation by

a regulator, which sets a minimum rating standard and the implications for social

welfare.

3.3 The Optimal Rating Standard

If rating quality is neither observable nor contractible, the CRA has an incentive

to lower the rating quality. This would decrease the costs per credit rating and

increase the CRA�s pro�ts, which again decreases the social value of a credit rating.

In order to preserve the potential social value added of a credit rating, a regulator

can set a minimum rating standard.19 In contrast to auditing �rms, CRAs so far

cannot be made liable for consequences of inaccurate credit ratings. This is because

credit ratings are regarded as an opinion, comparable to a report in a newspaper.

The only way to regulate CRAs would be, as in the model on hand, to supervise

the surrounding conditions of the rating process.20 We assume that a regulator

has a costly technology, which may detect whether a CRA incorporates a rating

19The content of minimum rating standards could for example be oversight of CRA�s sta¤,transparency of the rating process or parts of the IOSCO code of conduct fundamentals whichcan be summarized in three categories: 1. Quality and integrity of the rating process, 2. CRAindependence and 3. CRA responsibilities to the investing public and issuers. (see IOSCO, 2004)20Minimum quality standards would be for example prerequisites regarding the sta¤, the IT

systems or the organizational structure of CRAs.

16

quality below a certain minimum rating standard, which is set by the regulator.

The detection technology is designed in such a way that the regulator can detect

compliance with a rating standard with a certain probability h 2 [0; 1], which is an

increasing and concave function of the employed costly e¤ort e: h0 (e) > 0, h00 (e) < 0

and h (0) = 0, lime!1

h (e) � 1, lime!1

h0 (e) = 0, lime!0h0 (e) = 1. If the regulator detects

that the rating quality of a CRA is below the rating standard, the CRA has to pay

a penalty �. Since a deviating CRA will not be detected with certainty, it faces an

expected penalty P. The pro�t of the CRA is now given by the fee per rating minus

the costs per rating minus the expected penalty:

�CRA (q) = � (q)� c (q)� P

Lemma 1 describes the expected penalty in case of deviation and compliance with

the rating standard.

Lemma 1 If the regulator sets a rating standard q̂, and if deviation from the stand-

ard is detected with probability h (e), the CRA faces an expected penalty P with

P =

�h (e) �, if q < q̂

0, if q � q̂.

Since we assume limited liability of the CRA, the penalty � in case of deviation

from the rating standard and detection by the regulator has an upper limit. This

upper limit can be characterized by the total wealth W of the CRA, accumulated

from past activities plus the rating pro�ts in the actual period in the case of deviation

from the rating standard (i.e. c(q) = 0): � � W + �.

The sequence of events in the model is summarized in �gure 2. At �rst, nature

determines, whether the portfolio of the IB is good or bad. In the next step, the

regulator has to decide on the rating standard q̂, the penalty for the CRA in case of

deviation from the standard �, and the e¤ort employed in the detection technology

e. Taking the parameters, chosen by the regulator, as given, the IB decides to buy a

credit rating at quality q̂, if the informational value of the credit rating is larger or

equal zero and pays the rating fee �. Then the CRA decides on the rating quality q

and issues a credit rating (r = b or r = g). After the credit rating is published, the

17

Figure 2: Sequence of events.

regulator detects deviation from the rating standard with probability h(e) and the

CRA has to pay the penalty � in case of deviation from the standard. Debt �nance

d is being provided, conditional on the issued credit rating, and �nally, the value of

the portfolio (g or b) materializes.

We assume that the objective of the regulator is to maximize the social value

(V ) of the credit rating. If we take into account that regulation needs costly e¤ort

e, the decision problem of the regulator is to maximize the social value of the credit

rating, given by equation (4), minus the e¤ort costs of regulation e, by deciding on

the rating standard q, the detection e¤ort e and the penalty �:

maxq̂;e;�

V (q̂) = q (1� p)m� c (q)� e (6)

The incentive compatibility constraint that induces the CRA to comply with the

rating standard is given by:

� (q̂)� c (q̂)� P (q � q̂) � � (q̂)� c (q)� P (q < q̂) (7)

The incentive compatibility constraint states that the expected pro�t of the CRA in

case of compliance with the rating standard net of rating costs and expected penalty

must be larger or equal the expected pro�t in case of deviation from the standard

net of the expected penalty. Since in the case of deviation the CRA chooses the

lowest rating quality q = 0 in order to minimize costs (c (0) = 0), and since the

optimal policy of the regulator requires the incentive compatibility constraint to be

18

binding, equation (7) can be rewritten, using lemma 1, as:

c (q̂) = h (e) � (8)

The rating costs c are increasing and convex in q 2 [0; 1] and the probability that

regulation will detect deviation from the rating standard h (e), which could be con-

sidered as the e¢ciency of regulation, is monotonous increasing and concave in the

employed e¤ort e as we have de�ned above. Therefore, the function h (e) can be

inverted and equation (8) be solved for the optimal regulatory e¤ort, depending on

the quality standard q̂, and be rewritten as:

e (q̂) = h�1�c (q̂)

�

�(9)

This function reveals the optimal regulation e¤ort for a given quality standard, such

that the quality standard is implementable, meaning that the incentive compatibility

constraint is binding. For a given penalty and due to the assumed characteristics

of the cost function c(q), the optimal e¤ort, which is employed in regulation, is

increasing and convex in the rating standard q̂. The intuition of this equation is

straightforward. If the rating standard increases, the costs of rating increase, too.

Therefore, the incentive for a CRA to deviate from the standard (i.e. setting the

rating quality equal zero) increases. In order to make the higher standard incentive

compatible, the expected penalty must increase. For a given penalty �, the regulator

has to increase e¤ort e to implement the more demanding rating standard q̂. We

have mentioned above that due to limited liability, the penalty, the CRA has to

pay in case of deviation from the standard is limited by the wealth, accumulated

in the past plus the pro�ts of rating in the actual period. Furthermore, equation

(6) shows that e¤ort, employed in regulation, reduces social welfare. In order to set

the expected penalty such that the incentive compatibility constraint is binding, it

is optimal from a welfare perspective, to set the penalty in case of deviation to its

highest possible level: �̂ = W + �. A lower penalty would require the regulator to

employ more e¤ort to keep h (e) � constant, which would reduce social value.

19

The maximization problem of the regulator in equation (6) can now be reduced

to the optimal choice of the rating standard. The optimal penalty is given by �̂ and

the optimal e¤ort e is the optimal response to q according to equation (9). Inserting

equation (9) in equation (6) leads to:

maxq̂V̂ (q̂) = q̂ (1� p)m� c (q̂)� e (q̂)

Because rating costs and e¤ort costs are convex in the rating quality, the objective

function leads to an interior solution. The �rst-order condition is given by:

(1� p)m = c0 (q̂) + e0 (q̂) ;

which leads to the optimal rating standard that maximizes social welfare, under the

assumption that rating quality is unobservable. In part 3.2 we have shown that

the �rst-best rating quality in the case of observable and contractible rating quality

was given by (1� p)m = c0 (q�). A comparison with the optimal rating standard

under regulation shows that q̂ < q�. The intuition is straightforward. Monitoring of

a certain rating standard is costly, which reduces social welfare. Therefore a lower

rating standard compared to the �rst-best will be implemented by the regulator. The

in�uence of the exogenous parameters is analog to proposition 1 and are summarized

in proposition 2 point (i) to (iii). Additionally, the optimal rating standard is

increasing in the e¢ciency of regulation (i.e. the optimal rating standard is higher,

if the marginal e¤ort costs of increasing the standard are lower).

Proposition 2 A regulator, who maximizes social welfare, chooses a rating stand-

ard q̂ which is lower than the �rst-best rating standard q�. The optimal rating stand-

ard q̂ becomes

(i) smaller, if the unconditional probability of the IB�s portfolio being in a good

state p increases.

(ii) larger, if the size of the potential misallocation of investment m without

increases.

20

(iii) larger, if the cost e¢ciency of the CRA and the regulator increases.

(iv) The optimal rating standard q̂ is higher, if the wealth of the CRA increases.

Proof. See appendix A.2.

Part (iv) of proposition 2 implicitly points to the di¤erence in the optimal rating

standard in the case, where CRAs make zero pro�ts, i.e. "perfect competition" on

the CRA market, and the case, where CRAs takes the informational value of rating,

i.e. the "market power case" (see for these two cases part 3.2). In the market power

case (m), the wealth of the CRA that can be penalized by the regulator may be

assumed to be larger than the wealth in the perfect competition case (c). Therefore,

the optimal penalty, which is set by the regulator, would have the following property:

�̂m > �̂c. The modi�ed incentive compatibility constraint (9) shows that the optimal

regulatory e¤ort for a given rating standard is decreasing as the optimal penalty

increases. Therefore, enforcement of regulation becomes more e¢cient, if the CRA

has "more to lose", since less costly e¤ort has to be employed to enforce a given

rating standard. From this follows that costly regulatory e¤ort has a less negative

impact on social welfare. The optimal rating standard increases, if the representative

CRA has more to lose, i.e. if the CRA has a higher "charter value". The model

shows again that from this perspective, market power of some few CRAs is not in

itself a rationale for regulatory intervention. In the �rst-best case, where rating

quality is assumed to be observable and contractible, the optimal rating quality and

social value of ratings is independent of the structure of the CRA market. In the

case of unobservable rating quality, the model shows that a higher charter value of

CRAs moves the optimal rating standard and social value of credit ratings closer to

the �rst-best result.21

21However, even if this is true in the framework used here, this �nding should be read withcaution with regards to generalization. The only consequence of market power in the model is thatthe surplus of credit ratings is reallocated from the IB to the CRA, the overall surplus remainsunchanged. The model does not take into account potential adverse e¤ects of CRA market powerwith consequences on the level of the rating fee and the overall social value of credit ratings.Ine¢cient high rating fees might for example induce the debt issuer to engage in riskier portfolios,which may decrease �nancial market stability.

21

4 Con�icts of Interest and Optimal Regulation

So far, the unobservability of rating qualities was considered as the only rationale for

the regulation of CRAs. What has not yet been included in the model are potential

adverse e¤ects of con�icts of interest between the CRA and the rated �rm (in our

framework the rated IB). One potential source of con�icts of interest is the fact

that credit ratings usually are paid by the issuer of a debt instrument and not by

the investors. Facing the fact that since the early 197022 CRAs mainly are paid by

their clients23, the client could in principle directly bribe the CRA in exchange for

a better credit rating. Another potential con�ict of interest emerged in the special

role of CRAs in the rise of structured �nance products during the last years. While

interaction between the issuer of a traditional debt security and the CRA was rather

limited, the case is di¤erent in the rating of structured �nance transactions. In the

rating process of those structured �nance products, CRAs are involved in an iterative

process with the issuer. The structuring process of these products includes implicit

structuring advice by the CRAs, meaning that the CRA indicates what needs to be

done to receive the desired credit rating.24 Broadly speaking, CRAs not only o¤er

the service of the pure rating, but also o¤er additional consulting services. This

deeper involvement of CRAs has been heavily criticized in the public, especially

in association with the crisis in the subprime loan market. This problematic is

also captured to some degree in the U.S. "Credit Rating Agency Reform Act 2006",

which among others "directs the SEC to issue �nal rules to prohibit unfair, coercive,

or abusive acts or practices by NRSROs25 [...] such as conditioning or threatening

22For an overview on the history of credit rating agencies see for example Hill (2004) or Cantor& Packer (1995).23An argument for this payment scheme is the emergence of information technology during the

last 30 years, which gave information, once it is originated a public good character (a single investorwould only be willing to pay for a rating if it is not made public). Another argument is that it ismore e¢cient to let the issuer pay instead of each single investor of a large and dispersed investorcommunity, that uses the credit rating for its investment decision. (see White, 2001)24For a summary of the role of CRAs in structured �ncance products see Mason & Rosner (2007)

and BIS (2005). According to BIS (2005) "[...] it has become common for rating agencies to o¤erspecial services relating to �rms� bond ratings [...] that could impact rating levels. These servicesmay be separately rewarded and may thus exacerbate any potential con�icts of interst arising from�issuer fees�."25NRSRO = nationally recognized statistical rating organization; a CRA has to be recognized

by the SEC (securities and exchange commission), in order to be used for regulatory purposes. The

22

to condition an issuer�s credit rating on the purchase of other services or products"

(see CRA Reform Act, 2006). Based on Pagano & Immordino (2007) for the case of

auditing �rms, we extend in the following section the model by allowing the CRA to

o¤er additionally consulting services to the rated investment bank (IB). We assume

that the portfolio, for which the IB seeks debt �nance from external investors, is

managed by a portfolio-manager, who�s salary partly consists of a payment which

is proportionally to the volume of managed portfolios. Hence, the manager has an

interest that the IB receives �nancing by external investors with certainty, since

this would increase his salary. As we have shown above, external investors only

�nance a portfolio, if it receives a good credit rating (r = g), therefore the portfolio-

manager has an incentive to engage in activities to ensure a high credit rating for

the portfolio.26 One possibility to achieve that goal would be a direct bribe to the

CRA in exchange for a higher credit rating. Another way of modelling con�icts of

interest in our model arises from the joint provision of credit ratings and consulting

services by a single CRA, from which emerges a more sophisticated possibility of

collusion between the CRA and the rated IB as follows. Since the CRA is very well

informed about its client in the course of the rating process, we assume that the

CRA has the expertise to o¤er consulting services to the IB at lower costs compared

with competitors due to economies of scope. The possibility of collusion now arises,

if the IB is only willing to pay for an additional consulting contract, if in exchange

the CRA issues a good credit rating. Since we assume that the CRA can provide

such services at lower costs, the received market fee for the consulting service can be

regarded as a rent for the CRA. The con�ict of interest is clear: the consulting fee

acts as a bribe, and the CRA only gets the fee in exchange for a good credit rating.

Section 4.1 extends the model and analyzes consequences for the optimal rating

standard which is set by the regulator. In section 4.2, we analyze, if forbidding the

joint provision of rating and consulting services is optimal from a welfare perspective.

"Credit Rating Agency Reform Act 2006" includes the simpli�cation of the recognition process.26Note, that we assume that the IB decides to get rated only, if the informational value of a

credit rating is larger or equal zero (see section 3.1).

23

4.1 Optimal Rating Standard in the Presence of Con�icts

of Interest

The analysis is now extended by assuming that the IB employs a portfolio-manager,

whose salary consists of a proportion � 2 [0; 1] of the portfolio value. After de-

ducting the rating fee and repayment of debt to external investors, the net pro�t

of the IB after the true value of the portfolio materialized with consideration of

the management compensation, is given by: ~ � � � d � �~. According to the

compensation scheme, the manager has an interest that investment takes place with

certainty, which is the case without a credit rating and with a "good" credit rating

r = g. Therefore, the manager - if he is opportunistic - has an incentive to induce

the CRA to issue a good credit rating. The manager - who requires the CRA to issue

a good credit rating in exchange - may either bribe the CRA directly by o¤ering a

bribe � > 0 or indirectly by engaging the CRA for rating and additional consulting

services. In the following it will be shown that both forms of corruption have similar

implications regarding the optimal rating standard. The CRA is assumed to be able

to o¤er consulting services additionally to the rating service. Due to economies of

scope, the CRA is assumed to o¤er the same consulting service as an external com-

petitor (Comp:) at lower costs �: �CRA < �Comp:.27 Under the assumption of perfect

competition in the consulting sector, the market consulting fee ' is equal to the

consulting costs: ' = �Comp:. If the CRA, instead of an external �rm, gets employed

for performing the consulting service, the CRA receives the market consulting fee '

and therefore earns a rent �� � ' � �CRA > 0. At the same time, making use of

the CRA�s economies of scope, the rent �� increases social welfare, due to e¢ciency

gains.

Given those assumptions, the portfolio-manager has an incentive to o¤er a con-

sulting contract, contingent on a good credit rating. If the CRA accepts this o¤er,

the pro�ts of the CRA from rating and consulting are given as follows:

�CRA (q) = � (q)� c (q) + '� �CRA � P (10)

27From performing the rating procedure, we assume that the CRA has gained expertise to o¤eradditional consulting at lower costs, compared to a third competitior.

24

The requirement for getting o¤ered the contract for the joint provision of credit

rating and consulting is that the CRA issues a good credit rating. Therefore, it is

optimal for the CRA to set q = 0, since that minimizes the costs (i.e. c (0) = 0).

Using �� � ' � �CRA > 0 and considering the expected penalty in the case of

deviation from the rating standard h (e) �̂, equation (10) can be rewritten as:

�CRA (q) = � (q) + ��� h (e) �̂ (10�)

Now it is obvious that the additional rent for the consulting service acts as a bribe.

The bribe makes sure that the IB receives a good credit rating and that �nancing

by external investors happens for sure. Therefore, the portfolio-manager gets the

partial salary �~ with certainty. In the case of a direct bribe �, the pro�t equation

can be formulated analogously by replacing �� with �. While the consequences

of corruption regarding the social value are clear in the case of the direct bribe,

they are twofold in the case of joint provision of services. In both cases the IB

receives a good credit rating and the IB�s portfolio receives even then �nancing, if

the portfolio would have received a bad credit rating without the bribe. Henceforth,

the misallocation of funds increases, which reduces the social value of a credit rating.

An additional positive impact on the social value occurs with the joint provision of

services, because the CRA is assumed to o¤er consulting services more e¢ciently in

terms of costs compared to a third party. Therefore, the social value increases by

�� in that case. We assume that the possibility of collusion cannot be prevented

by the external investors, since the large investors community is assumed to have

a collective action problem.28 Taking into account the opposed e¤ects of the joint

provision of services by a single CRA and the possibility of collusion, the decision

problem of the regulator, who maximizes the social value of rating, is given by29:

max~q;e

~V (~q) = ~q (1� p)m+��� c (~q)� e (11)

28If any collective action restrictions would be absent, investors could make the debt �nancingdependend on the requirement, that consulting and rating by the same �rm is impossible.29The e¢ciency gain is integrated into the social value function in the most easiest way by simply

adding ��. In the case of a direct bribe � the positive e¤ect on social welfare would be absent andthe objective function of the regulator is the same as equation (5) in section 3.3.

25

The rating standard in the presence of possible collusion is denoted by ~q. The

new incentive compatibility constraint requires the CRAs pro�t from rating and

compliance with the rating standard, set by the regulator, to be larger or equal the

CRAs pro�t in the case of joint provision of services and acceptance of the bribe,

given by equation (10�):

� (~q)� c (~q) � � (~q) + ��� h (e) �̂

In the case of a direct bribe, �� in the incentive compatibility constraint has to

be replaced by �. The optimal rating standard has to be chosen such that it is

implementable by the CRA and collusion does not happen. According to section

3.3, the incentive compatibility constraint can be reformulated as the optimal e¤ort,

employed in regulation, as a function of the optimal rating standard, which assures

the constraint being binding:

e (~q) = h�1�c (~q) + ��

�̂

�(12)

As equation (9) in section 3.3.3, the optimal e¤ort is increasing and convex in the

rating standard. But in contrast to equation (9), the optimal e¤ort, given a certain

rating standard is now higher, since the numerator increases by �� in equation

(12).30 In that case, more costly e¤ort has to be employed by the regulator to make

a given rating standard incentive compatible. Using equation (12) in equation (11),

maximizing with respect to ~q leads to the following �rst order condition:

(1� p)m = c0 (~q) + e0 (~q)

Proposition 3 describes the properties of the new optimal rating standard:

Proposition 3 If the rent from the joint provision of services is �� > 0 or if

there is the possibility of a direct bribe � > 0, the optimal rating standard in the

presence of potential collusion between CRA and IB is lower than the optimal rating

30Analogously, in the case of a direct bribe the optimal e¤ort, which assures the incentive com-

patibility constraint being binding, can be rewritten as: e (~q) = h�1�c(~q)+��̂

�.

26

standard without the possibility of collusion: ~q < q̂. The optimal rating standard

is decreasing, if the rent of the joint provision of services �� or the direct bribe �

increase.

Proof. See appendix A.3.

If there were no e¢ciency gains from the joint provision of services, the bribe

would be zero: �� = 0. In that case the optimal rating standard is the same as in

section 3.3., where rating service only is considered: ~q = q̂. Accordingly, the optimal

rating standard is the same (~q = q̂), if the regulator would forbid the joint provision

of services by the CRA or the possibility of a direct bribe, since the possibility of

collusion would then be eliminated. The intuition of why ~q < q̂ is straightforward, if

�� > 0 or � > 0. The corresponding e¤ort that has to be employed by the regulator

for a given rating standard is now higher as shown in equation (12). Since an increase

of costly regulatory e¤ort decreases the social value, the regulator chooses a lower

rating standard. If the rent �� or the direct bribe � increase, also the incentive

for the CRA to accept the bribe and collude with the IB increases. Therefore it

is optimal for the regulator to set a lower rating standard, since that would reduce

the CRA�s cost in the case of compliance with the standard. In principle, one of

the two sources of potential collusion can be prevented by the regulator by simply

forbidding the joint provision of rating and consulting services. That issue has

also been discussed by the SEC and the European Commission in reaction to the

inglorious role of CRAs in the subprime loan crisis in 2007 and been addressed in

the "Credit Rating Agency Reform Act 2006" in the US. While collusion through

the joint provision of services cannot be presumed ex ante by the regulator, the

intention for corruption is obvious for the case of a direct bribe. For the remainder

of the paper is assumed that direct bribes, for example in the form of extra payments

or rating fees above the market level, would easily be detectable by the regulator

and the analysis concentrates on the more sophisticated form of collusion - namely

con�icts of interest via the joint provision of services. Whether the joint provision

of services should be prohibited by regulation from a welfare perspective, will be

analyzed in the next section.

27

4.2 Regulatory Intervention and Social Value

The model showed that the consulting fee can be used by the client to bribe the

CRA to issue an inaccurate higher credit rating, if a CRA o¤ers both ratings and

consulting services. As already mentioned above, the role of CRAs in the past years

changed from a passive to a more active part particularly in the rating process of

structured debt products, such as collateralized debt obligations. In an iterative pro-

cess, CRAs are involved in advising their clients in designing products that receive

the desired high credit rating to be attractive for the investors community. CRAs

have been heavily criticized for this behavior in the recent past, as they were under

suspicion of being exposed to con�icts of interest, therefore being jointly respons-

ible for the �nancial market crisis in 2007 by issuing inaccurate credit ratings. The

model�s answer to a situation with existing con�icts of interest is that the regulator

should either simply choose a lower rating standard or forbid the joint provision of

services and eliminate the potential con�ict of interest at its root. In the latter case

the regulator chooses optimally a higher rating standard, as shown in the previous

section. But what has not been analyzed so far, is the question, whether the regu-

lator should allow of forbid the joint provision of services, if the decision criterion is

the social value.31 The objective function of the regulator in the presence of con�icts

of interest was given by:

max~q

~V (~q) = ~q (1� p)m+��� c (~q)� h�1�c (~q) + ��

�̂

�(13)

As we have shown above, the CRA - if it is hired for creating a credit rating - can

provide consulting services more e¢ciently in comparison to external competitors

by being able to provide the same service at lower costs. This e¢ciency gain ��,

that can be used by the rated IB to bribe the CRA, on the one hand increases the

social value. This positive e¤ect would be lost, if the regulator would forbid the

joint provision of services. On the other hand, the joint provision of services makes

31In the case of a direct bribe (�) without joint provision of services, the implication for regulationis very easy: "forbidding" to accept the direct bribe increases the social value of rating, becausethere is no potential e¢ciency gain and no trade-o¤ from allowing the possibility of collusion inthat case.

28

collusion possible and the �nancing of bad portfolios more likely, which decreases

the social value. As the e¢ciency gain has one negative and one positive e¤ect

on the social value, the answer is now, under which circumstances the regulator

optimally should allow or forbid the joint provision of activities. If the regulator

forbids the bundling of services, the social welfare of the credit rating is V̂ (q̂), as

de�ned in section 3.3. In the following, we compare the social value in the case of

joint provision of services (case 1: ~V (~q)), with the social value, if CRAs are allowed

to o¤er ratings only (case 2: V̂ (q̂))32. The partial e¤ect of an increase of �� on the

social value in case 2 is zero (@V̂ =@�� = 0), while in case 1 is given by

@ ~V

@��= 1� h�10 (:::)

1

�̂(14)

Depending on the size of equation (14), i.e. whether 1 ? h�10 (:::) 1�̂, the social value

can either increase or decrease as �� increases. Therefore, obviously one criterion

for the regulator�s decision is the size of ��, as the e¤ect on the social value could

be positive or negative for di¤ering values. The previous section has shown that

the necessary e¤ort for a given rating quality increases as �� becomes larger. From

this follows that h�10 (:::) in equation (14) is a positive and increasing function of

��. If equation (14) is negative at �� = 0, it remains negative for any �� > 0. In

that case, despite of the e¢ciency gain, it is optimal for the regulator to prohibit

the joint provision of services, because ~V < V̂ for all �� > 0. If equation (14) is

positive at �� = 0, it becomes negative, if �� becomes su¢ciently large. In that

case, there exists a threshold value for the size of �� = ���, below which it is

optimal for the regulator to allow the joint provision of services (case 1), since the

positive e¤ects on the social value overweigh (~V � V̂ for 0 � �� � ���). On the

other side for �� > ��� it is optimal to forbid the joint provision of ratings and

consulting services, since the adverse e¤ects of con�icts of interest dominate (~V < V̂

for�� > ���). To analyze the determinants for the decision of the regulator, besides

the size of the e¢ciency gain (which works in our model as a bribe) further, equation

32The objective function if the CRA o¤ers the service of rating only was given by V̂ (q̂) =

q̂ (1� p)m� c (q̂)� h�1�c(q̂)�̂

�(see section 3.3).

29

(14) can be rewritten as follows33:

@ ~V

@��=

1

c0 (~q)(c0 (~q)� e0 (~q)) (15)

Equation (15) is negative for any positive value of ��, if c0 (~q) < e0 (~q) at �� = 0.

While c0 (~q) can be interpreted as the marginal costs of rating, and therefore as the

cost e¢ciency of CRAs, e0 (~q) can be interpreted as the e¢ciency of the regulation

technology. Above, the regulation technology was characterized by the probability

to detect deviation from a certain rating standard by employing costly e¤ort e. A

more e¢cient regulation technology would require less e¤ort to enforce a given rating

standard and henceforth a lower increase of e¤ort if the rating standard increases

(e0high (~q) < e0low (~q)). If the e¢ciency of the rating technology is su¢ciently low,

such that c0 (~q) < e0 (~q) at �� = 0, it is optimal for the regulator to forbid the

joint provision of services for any positive value of ��, since the social value in

case of the joint provision of services is always smaller, compared to case 2 (~V (~q) <

V̂ (q̂)). Proposition 4 describes the optimal decision of the regulator, if the regulation

technology is too ine¢cient.

Proposition 4 If the regulation technology is su¢ciently ine¢cient, such that

c0 (~q) < e0 (~q) at �� = 0, the optimal strategy for the regulator is to forbid the

joint provision of services and to set the optimal rating standard q = q̂. Otherwise

the social value of rating would be ine¢ciently low for any �� > 0: ~V (~q) < V̂ (q̂).

Proof. See appendix A.4.

While the decision between case 1 and case 2 is clear and independent of the

size of ��, if c0 (~q) < e0 (~q) at �� = 0, the decision problem looks di¤erent, if the

e¢ciency of the regulation technology is su¢ciently high. If the regulation techno-

logy is such that c0 (~q) > e0 (~q) at �� = 0, equation (15) is positive as �� increases

and becomes negative, if �� becomes su¢ciently large. This is true, because c0 (~q)

33The derivation of equation (15) is located in appendix B.

30

becomes smaller and e0 (~q) becomes larger as �� increases.34 From this follows that

for c0 (~q) > e0 (~q) at �� = 0 the optimal decision of the regulator for one of the two

alternatives depends on the size of the e¢ciency gain ��. Proposition 5 describes

the optimal decision of the regulator.

Proposition 5 If the regulation technology is su¢ciently e¢cient such that c0 (q̂) >

e0 (q̂) at �� = 0, and the size of the e¢ciency gain is below its critical value, �� <

���, the optimal strategy for the regulator is to allow the joint provision of services

and to set the optimal rating standard ~q < q̂, since ~V (~q) > V̂ (q̂) for �� < ���. If

the e¢ciency gain is larger than its critical value, �� > ���, the optimal strategy

is to forbid the joint provision of services and to set the optimal rating standard q̂,

since ~V (~q) < V̂ (q̂) for �� > ���.

Proof. See appendix A.5.

The model shows that the joint provision of services - for example expressed by

the deep involvement of CRAs in the rating process of structured �nance products,

such as collateralized debt obligations - is not necessarily a root of ine¢ciency for

which regulatory intervention could be justi�ed. If the criterion for the regulator

is social welfare, the decision of the regulator on the optimal rating standard and

possible restrictions of activities depends on the surrounding conditions. If the

potential bribe is large enough, it is optimal to restrict the activities of CRAs, as

the negative e¤ects of collusion dominate.35 But it could be optimal to allow the

joint provision of services, if the bribe is low enough, since the positive e¤ects of

the e¢ciency gain dominate in that case. Additionally, the model shows that the

basic requirement for the strategy of allowing the joint provision of services lies in

34Proposition 3 in the previous section has shown that @~q@�� < 0. Because of the convexity of c(:)

follows that @c0(:)

@�� < 0. For the derivation of@e0(:)@�� , see the proof of proposition 4 in the appendix.

35One implication of the model is to forbid the joint provision of services if consulting servicescould be provided very e¢ciently (i.e. if �� > ���). The argument is that in those cases theincentive of the CRA to collude with the IB is so high such that the social value of ratings becomesine¢ciently low. A possibility to get rid of the collusion problem and to pro�t from the welfareincreasing e¢cient provision of consulting services would be for the CRA to create �rewalls andfor the regulator to check their e¤ectiveness. The integration of this aspect in the model is onepossible extension for future research.

31

the hand of the regulator, meaning that the e¢ciency of the regulation technology

has to be su¢ciently high.

5 Conclusion

The discussion on the role and power of CRAs in �nancial markets is an ongoing

debate among academics, practitioners, and institutions of �nancial supervision.36

Many times, CRAs were suspected for having issued inaccurate credit ratings or

having updated already issued credit ratings too late. Furthermore, CRAs were

suspected to be exposed to various con�icts of interest. Jochen Sanio, the chairman

of the German federal �nancial supervision authority (Ba�n), once blamed CRAs

to be the "largest uncontrolled power in the global �nancial system".37 On the role

of CRAs in the subprime loan crisis, Keneth Rogo¤ presumed that ""[...] rating

agencies cooperated too closely with the banks and received a much too high pay-

ment for their ratings." and "I could imagine that Moody�s will become the Arthur

Andersen of this decade"(see Zeit, 2007).

The applied model, which is based on Pagano & Immordino (2007), has shown

that intransparency of how credit ratings are generated by CRAs, could be a ra-

tionale for regulation. Without regulation, the quality of the credit ratings would

be ine¢ciently low and misallocation of investment ine¢ciently high. Minimum

rating standards, which can be enforced by costly regulation, would increase the

social value of credit ratings in the applied model. The adverse e¤ects of con�icts

of interest were analyzed in the model, too. By the joint provision of credit ratings

and consulting services, we have shown that on the one hand there is the threat of

collusion, which may lead to inaccurate credit ratings, but on the other hand that

potential e¢ciency gains are present, too. In the presented theory, the potential con-

�ict of interest can be prevented by simply constraining the activities of CRAs. It

has also been discussed that this regulatory intervention may or may not be optimal

36See for example IOSCO (2004, 2007) and CRA Reform Act (2006).37Own translation from German to English. This quote is from a public hearing of the �nancial

committe of the German Bundestag at June 4th 2003.

32

from a welfare perspective.

The results of that paper on the one hand gives a contribution to the theoretical

academic literature on CRAs, by modelling the optimal regulation of CRAs in the

presence of unobservable rating quality and con�icts of interest. On the other hand,

the analysis, presented in this paper, also contributes to the discussion about the

possibility and necessity to regulate activities of CRAs that is consistently present

among institutions of �nancial market regulation as well as observers and practi-

tioners of �nancial markets, especially in the aftermath of the subprime loan crisis

in 2007. A frequent argument against regulation of CRAs in the past was that

CRAs have a strong incentive to issue accurate credit ratings, because otherwise

they would lose their reputation, which is regarded to be the most important asset

of CRAs.38 Therefore it was argued that self-regulation among CRAs works well

and no further regulation would be necessary.

However, a necessary requirement for self-regulation is competition and the pos-

sibility of market entry for competitors. Due to the market power of some few

CRAs and the heavy criticism, CRAs were confronted with in the past, it is disput-

able whether the threat of losing reputation is enough to prevent CRAs from issuing

inaccurate credit ratings and colluding with debt issuers. Regarding this limited

competition, Partnoy (1999) argues that markets may become inattentive as to the

CRAs� reputation as soon as some few CRAs have received recognition status by the

regulator. As soon as self-regulation of CRAs fails, the results of our paper provide

insights for the optimal regulation of CRAs.

38see for example Schwarcz (2001).

33

Appendix

A Proofs of Propositions

A.1 Proof of proposition 1.

The optimal rating quality q� 2 [0; 1] is derived by the �rst order condition:

(1� p)m = c0 (q�) (A1.)

E¤ect of p: As p increases, the left hand side of A1. becomes smaller. To keep

equality, the right hand side has to become smaller, too. Due to the characteristics

of the cost function c(:), the optimal rating quality q� has to decrease.

E¤ect of m: m increases, if d increases and/or b decreases. The left hand side

increases, therefore the optimal rating quality q� has to increase, too.

E¤ect of c0 (q�): A more e¢cient rating technology is expressed with lower costs

for a given rating standard. If rating quality increases, the rise of costs is lower for a

more e¢cient technology: c0high (�q) < c0

low (�q). The marginal rating costs for a given

rating quality is lower, if cost e¢ciency becomes higher. The value of left hand side

is exogenous and constant. If cost e¢ciency increases q�, the rating standard has to

rise in order to keep the right hand side constant.�

A.2 Proof of proposition 2.

The optimal rating standard if rating quality q̂ is unobservable and with costly

regulation is derived by the �rst order condition:

(1� p)m = c0 (q̂) + e0 (q̂) (A2.)

34

As the left hand side of (A2.) is the same as the left hand side of (A1.), we have:

c0 (q�) = c0 (q̂) + e0 (q̂) (A.2�)

Since c(:) and e(:) are increasing and convex in q, therefore q� has to be larger than

q̂: q� > q̂.

For the proof of parts (i) to (iii) of proposition 2 see the proof of proposition

1. Part (iv) claims that the optimal rating standard is higher, if optimal penalty �̂

increases. An example for a rise in �̂ is an increase in the pro�ts per rating due to

market power in the CRA sector. The necessary e¤ort that has to be employed in

order to enforce a given rating standard, is given by:

e (q̂) = h�1�c (q̂)

�̂

�(A3.)

If �̂ increases, the optimal e¤ort corresponding to a given rating standard decreases.

From this follows that the marginal e¤ort e0(:) decreases either. The right hand side

therefore becomes smaller for a given rating standard. Due to the characteristics of

the functions c(:) and e(:), the optimal rating standard q̂ must increase to ensure

equality of equation (A.3).�

A.3 Proof of proposition 3.

Why the optimal rating standard in the presence of joint provision of services (~q) and

analogously in the case of a direct bribe, is lower than the optimal rating standard in

3.3 (q̂), can be shown as follows: The �rst-order condition of the regulator�s decision

problem is given by

(1� p)m = c0 (~q) + e0 (~q) (A.4)

The left hand side of A4. the same as in equation A.2, therefore it must be true

that:

c0 (q̂) + e0 (q̂) = c0 (~q) + e0 (~q) (A.4�)

35

Since the e¤ects are analog for the direct (�) and the indirect bribe (��), the proof

is presented for �� > 0 only. Taking into account the potential bribe ��, the

necessary e¤ort to enforce a given rating standard �q is larger in the case of joint

provision of services:

e (�q) = h�1�c (�q)

�̂

�< e (�q) = h�1

�c (�q) + ��

�̂

�

The marginal e¤ort with bribe is therefore larger than the marginal e¤ort without

bribe for a given rating quality. Therefore the optimal rating standard has to be

lower in the case of joint provision of services, to ensure equality of equation (A.4�),

given the characteristics of c(:) and e(:): ~q < q̂.

That the optimal rating standard is decreasing as the rent of the joint provision

of services increases can be shown by total di¤erentiating equation (A.4) and using

e0 (~q) = h0�1�c(~q)+��

�̂

�c0(~q)�̂:

d (1� p)m| {z }=0

= c00 (~q) d~q + e00 (~q) d~q + h00�1�c (~q) + ��

�̂

�c0 (~q)

�̂2d��

�!d~q

d��= �

h00�1�c(~q)+��

�̂

�c0(~q)

�̂2

c00 (~q) + e00 (~q)< 0 (A.5)

Equation is smaller than zero, because of the convexity of e(:), c(:), and h�1(). �

A.4 Proof of proposition 4.

The social value with joint provision of services is given by ~V , whereas the social

value with rating only is given by V̂ . If �� = 0, then ~V = V̂ . Equation (A.5)

showed that d~qd��

< 0. Therefore, given the characteristics of c(:), it must be true that

@c0(~q)@��

< 0. Above, we have shown that e0 (~q) = h0�1�c(~q)+��

�̂

�c0(~q)�̂. Di¤erentiating

with respect to �� yields @e0(~q)@��

= h00�1�c(~q)+��

�̂

�c0(~q)

�̂2> 0. The partial derivative of

the social value ~V and V̂ with respect to �� is given by: @ ~V@��

= 1c0(~q)

(c0 (~q)� e0 (~q))

and @V̂@��

= 0. As �� increases, the di¤erence (c0 (~q)� e0 (~q)) decreases, since c0

decreases and e0 increases. If @ ~V@��

< 0 at �� = 0, which is the case if c0 (~q) < e0 (~q),

36

the social value ~V decreases further as �� increases. Therefore, it is optimal to

prevent the joint provision of services for any �� > 0, since ~V < V̂ . �

A.5 Proof of proposition 5.

If @ ~V@��

> 0 at �� = 0, then we must have c0 (~q) > e0 (~q). From this follows that

~V increases, if �� becomes larger, as long as �� is relatively small. Given the

characteristics of @c0(~q)@��

and @e0(~q)@��

, ~V decreases, for relatively large values of ��.

Therefore, at some critical level �� = ���, we have ~V = V̂ . For values �� < ���,

we have ~V > V̂ , and therefore allowing the joint provision of services is optimal.

For values �� > ����, we have ~V < V̂ , and therefore forbidding the joint provision

of services is optimal.�

B Derivation of Equation (15)

The necessary regulation e¤ort for a given rating standard is given by: e (~q) =

h�1�c(~q)+��

�̂

�. Di¤erentiating with respect to ~q leads to e0 (~q) = h0�1

�c(~q)+��

�̂

�c0(~q)�̂

and after rearranging:e0 (~q)

c0 (~q)= h0�1

�c (~q) + ��

�̂

�1

�̂(A.6)

Inserting equation (A.6) into equation (14): @ ~V@��

= 1 � h0�1�c(~q)+��

�̂

�1�̂leads to

equation (15):

@ ~V

@��= 1�

e0 (~q)

c0 (~q) !

@ ~V

@��=

1

c0 (~q)(c0 (~q)� e0 (~q))

37

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